I haven't shot one yet. But... I did have one in my hand last week. MKIII? MKII.. Other than a couple of new features, it's still a MKII when it comes to the barrel, frame design and trigger. That said, these .22's are capable of shooting very well. And they are very durable. I wish they had a left side cutout opening at the reciever like the Smith or the Buckmark. These things operate longer keeping cleaner when that modification is done to them. When I was looking at this particular MKIII, I was compairing to a MKII. I bought the MarkII in 6 1/2" stainless slab side. Competition Target model. The new features of the MKIII weren't enough to get me past sticker shock. Especially since I already have a MKII 4". My current older style magazines will work with the older model. Not so with the MKIII. Other than that, There's really no difference in the pistols when it comes to durability or accuracy.
If you don't own a MKII, then I'd say go for the MKIII. Out of the box, a Browning Buckmark will have a better feeling trigger, but the Ruger has many more aftermarket options when it comes to trigger modifications. I highly suggest extremely nice, but the Trapper for the price is very nice.
-Steve